Question

How much how much work should be done on a bicycle of mass 20 kg to increase its speed from 2 metre per second to 5 m per second?

Answer 1

Given mass of the bicycle m = 20 kg

Initial velocity of the bicycle = 2 m/s

Final velocity of bicycle = 5 m/s

We know,

Change in kinetic energy = Work done -----(A)

ΔK.E = K.E₂ - K.E₁

K.E₁ = (1/2) (20)(2)² = 40 J

K.E₂ = (1/2) (20)(5)² = 250 J

Reducing the above found values in A we get,

250 - 40 = Work done

Work done = 210 J

Answer 2

Solutions:

We know that whenever work is done, an equal amount of energy is used up. So, the work done in this case will be equal to the change in kinetic energy of bicycle when its speed changes from 2 m/s to 5 m/s.

(a) In the first case;

Mass of bicycle, m = 20 kg

And, speed of bicycle, v = 2 m/s

So, kinetic energy, Ek = 1/2mv^2

=> 1/2 × 20 × (2)^2

=> 10 × 4

=> 40 J

(b) In the second case;

Mass of bicycle, m = 20 kg

And, speed of bicycle, v = 5 m/s

So, kinetic energy, Ek = 1/2mv^2

=> 1/2 × 20 × (5)^2

=> 10 × 25

=> 250 J

Now, Work done = Change in kinetic energy.

=> 250 - 40

=> 210 J

Thus, the work done is 210 J.